Optimal control design for aircraft antiskid brake control systems

ABSTRACT

The optimal control design for antiskid brake control uses a discrete Kalman filter scheme in combination with a conventional aircraft brake control system, comprising sensors for measuring a speed of a wheel and brake torque, and for providing output signals indicative of the speed and torque values, and an optimal antiskid braking controller. The optimal antiskid brake controller includes a wheel speed filter, a reference velocity module, an optimal controller, and an integrator module. The optimal controller includes a discrete Kalman regulator utilizing a discrete Kalman filter, which compels the wheel velocity to quickly converge to the reference velocity, while the integrator produces appropriate antiskidding control and compensates for low frequency torque disturbances. The discrete Kalman filter estimates brake pressure, and the difference between the wheel velocity and a reference velocity, and these estimated states are regulated by a control feedback gain matrix. The weighting matrices and all gains are precalculated, and performance of the controller can be improved by adjustment of these factors. The optimal brake control design methodology can also be applied to an electric brake control system with slight modification of dynamic model parameters, gain values and weighting factors. This optimal brake control scheme provides for improvement of antiskid brake efficiency, and control tuning of a conventional aircraft brake control system.

BACKGROUND OF THE INVENTION

1. Field of the Invention

This invention relates generally to aircraft braking systems, and moreparticularly concerns a method and system for antiskid control of brakeassemblies of an aircraft, utilizing a discrete Kalman filter combinedwith reference velocity and integrator modules. The present new optimalcontroller compels the wheel velocity to quickly converge to thereference velocity.

2. Description of Related Art

A conventional skid detection system used in aircraft braking systemstypically includes a wheel speed transducer for each wheel brake of thewheels of the aircraft, for measuring wheel speed and generating wheelspeed signals that are a function of the rotational speed of the brakewheel. The wheel speed signal is typically converted to a signalrepresenting the velocity of the aircraft, and compared with a desiredreference velocity, to generate wheel velocity error signals indicativeof the difference between the wheel velocity signals from each brakedwheel and the reference velocity signal. The output of the velocitycomparator is referred to as velocity error. The velocity error signalsare adjusted by a pressure bias modulator (PBM) integrator, aproportional control unit, and a compensation network, and the outputsof these are summed to provide an antiskid control signal received bythe command processor. The PBM integrator in the antiskid loop dictatesthe maximum allowable control pressure level during braking. When noskid is detected, this integrator allows full system pressure to thebrakes.

The conventional PID controller for aircraft brake control systems dealswith various conditions such as aerodynamics, landing gear dynamics,μ-slip profile, different landing conditions, and the like. One majorproblem is that tuning of controller parameters to guarantee highefficiency in different landing conditions and conditions affecting thetire-runway coefficient of friction (μ) of the aircraft braking systemis often a difficult task.

In the modern state space optimal controller design for the aircraftbrake control systems, some efforts to utilize Kalman filter techniquesare noted that attempt to provide some advantages such as an estimationof a peak in a mu-slip curve of the tire-runway coefficient of friction,estimation of the optimal slip value, and the like. However, controlsystem observability and controllability continue to be a problem withcomplex tire-runway μ conditions, aerodynamics, nonlinear landing geardynamics, various landing conditions, and the like, and successfulsimulation results have not been demonstrated even in extremelysimplified dynamic models. Therefore, it would be desirable to provide anew optimal antiskid brake control method and system implementing anappropriate Kalman type optimal controller to provide an improvedantiskid brake efficiency and improved braking control tuning incombination with a conventional PBM integrator for aircraft brakecontrol systems. The present invention meets these and other needs.

SUMMARY OF THE INVENTION

Briefly, and in general terms, the present invention provides for animproved system and method for antiskid braking control implementing anoptimal filter control methodology in combination with a conventionalPBM aircraft brake integral control system. An optimal antiskid brakingcontroller is provided that includes a wheel speed filter, a referencevelocity module, an optimal controller, and a PBM integrator module. Theoptimal controller includes a discrete Kalman regulator utilizing aKalman filter, which compels the wheel velocity to quickly converge tothe reference velocity, while the integrator module produces appropriateantiskidding control and compensates for low frequency torquedisturbances. The optimal controller estimates brake pressure, and thedifference between wheel velocity and a reference velocity, and theseestimated states are regulated by a control feedback gain matrix. Theweighting matrices and all gains are precalculated, and performance ofthe controller can be improved by adjustment of these factors. Thesystem and method of the invention can also be applied to an electricbrake control system with slight modification of dynamic modelparameters, gain values and weighting factors. The optimal antiskidbraking controller of the invention allows for improvement of antiskidbrake efficiency, and improvements in controlled tuning of theconventional PID aircraft brake control system.

The invention accordingly provides for an improvement in a system forcontrolling braking of an aircraft during landing, the system includingwheel velocity signal generating means for producing a wheel velocitysignal that is a function of the rotational speed of the wheel, andmeans for measuring brake torque applied to a wheel brake of theaircraft. Typically, the wheel velocity signal generating meanscomprises a wheel speed filter for generating a filtered wheel velocitysignal based upon the wheel velocity signal. The system for controllingbraking of an aircraft during landing includes a velocity referencegenerator for generating a reference velocity signal indicating adesired reference velocity, aircraft velocity comparison means forcomparing the wheel velocity signal with the reference velocity signalfor generating a velocity error signal indicative of the differencebetween the aircraft wheel velocity signal and the reference velocitysignal, and an optimal brake controller for generating an optimal brakepressure control signal for the wheel of the aircraft to cause theaircraft wheel velocity to converge to the reference velocity, basedupon an estimated command brake pressure and an estimated value of acoefficient of friction between the tire and runway surface. A pressurebias modulator integrator is provided that is responsive to the wheelvelocity signal and the reference velocity signal to provide an antiskidcontrol signal, and means are provided for summing the optimal brakingcommand signal and the antiskid control signal to produce the commandbrake pressure signal.

In a presently preferred embodiment, the optimal brake controllercomprises a discrete Kalman regulator for determining the estimatedcommand brake pressure and the estimated value of the coefficient offriction. The discrete Kalman regulator, in a preferred aspect of theinvention, comprises a control feedback gain matrix and a Kalman filter,the Kalman filter receiving the velocity error signal and a brake torquefeedback signal, and the Kalman filter generating an estimated velocityerror signal and an estimated brake pressure, and the control feedbackgain matrix receives the estimated velocity error signal and theestimated brake pressure to generate the estimated command brakepressure and the estimated value of the coefficient of friction betweenthe tire and runway surface. In another presently preferred aspect, theoptimal brake controller determines the optimal brake pressure controlsignal based upon the estimated value of the coefficient of frictionbetween the tire and runway surface, the weight per wheel, the rollingradius of a tire, the reciprocal of the torque vs. pressure ratio, andthe estimated command brake pressure.

The present invention similarly provides for an improvement in a methodfor controlling braking of an aircraft during landing. The methodincludes the steps of generating a wheel velocity signal that is afunction of the rotational speed of a wheel of the aircraft, andapplying a command brake torque signal based upon a command brakepressure to the wheel brake of the aircraft. The method also typicallyinvolves filtering the wheel velocity signal to generate a filteredwheel velocity signal. A reference velocity signal is generatedindicating a desired reference velocity, the wheel velocity signal iscompared with the reference velocity signal for generating a velocityerror signal indicative of the difference between the aircraft wheelvelocity signal and the reference velocity signal, and an optimal brakepressure control signal is generated for the wheels of the aircraft tocause the aircraft wheel velocity to converge to the reference velocity,based upon an estimated command brake pressure and an estimated value ofa coefficient of friction between the wheel and runway. The estimatedcommand brake pressure and the estimated value of the coefficient offriction are determined with a discrete Kalman regulator, an antiskidcontrol signal is provided; and the optimal braking command signal issummed with the antiskid control signal to produce a command brakepressure signal.

In a presently preferred embodiment of the method, the discrete Kalmanregulator comprises a control feedback gain matrix and a Kalman filter,the Kalman filter receives the velocity error signal and a brake torquefeedback signal, and the Kalman filter generates an estimated velocityerror signal and an estimated brake pressure. The control feedback gainmatrix receives the estimated velocity error signal and the estimatedbrake pressure to generate the estimated command brake pressure and theestimated value of the coefficient of friction. In a preferred aspect,the step of determining the optimal brake pressure control signal isbased upon the estimated value of the coefficient of friction, theweight per wheel, the rolling radius of a tire, the reciprocal of thetorque vs. pressure ratio, and the estimated command brake pressure.

These and other aspects and advantages of the invention will becomeapparent from the following detailed description and the accompanyingdrawings, which illustrate by way of example the features of theinvention.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a schematic diagram of an optimal antiskid braking controlsystem according to the invention.

FIG. 2 is a schematic diagram of an optimal controller for determiningan optimal brake pressure control signal for the optimal antiskidbraking control system of FIG. 1.

FIG. 3 is a discrete Kalman regulator of the optimal controller of FIG.2.

FIG. 4 is an augmented linearized state equation for the optimalantiskid braking control system of FIG. 1.

FIG. 5 is a graphical comparison showing the convergence of the wheelvelocity and aircraft velocity for B717 parameters using the optimalantiskid braking control system and method of the invention with areference velocity of 245 fps.

FIG. 6 is a graphical comparison showing the actual and estimated statesfor the difference between wheel velocity and reference velocity (e) andbrake pressure (p_(b)) for B717 parameters using the optimal antiskidbraking control system and method of the invention with a referencevelocity of 245 fps.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

While automatic braking systems for commercial aircraft commonlyoptimize braking efficiency by adapting to runway conditions and otherfactors, tuning of controller parameters to guarantee high efficiency indifferent landing conditions and conditions affecting the coefficient offriction (μ) of the aircraft braking system on landing is oftendifficult. This and other problems concerning complex μ conditions,aerodynamics, nonlinear landing gear dynamics, various landingconditions can be addressed by an optimal antiskid braking controlmethod and system implementing an optimal filter control methodologyaccording to the present invention.

In the method and system according to the present invention, a brakecontroller having a new optimal controller utilizing a discrete Kalmancontrol scheme is combined with reference velocity and an integratormodule to provide improved brake control for automatic braking systemsfor commercial aircraft. In general terms, the new optimal controllercompels the wheel velocity to quickly converge to the referencevelocity, while the integrator produces appropriate skidding control andcompensates for low frequency torque disturbances and other extraneousfactors. The Kalman filter estimates the two states of brake pressureand a velocity error signal (e) indicative of the difference between theaircraft wheel velocity signal and the reference velocity signal, andthese estimated states are regulated by a control feed back gain matrix.This Kalman filter is further developed and constitutes a new optimalcontroller with manipulation of an estimated coefficient of friction (μ)between the tire and runway surface. The weighting matrices and allgains are precalculated and performance of the controller is improved byadjustment of these factors. Although an exemplary first order hydraulicmodel is described for use with a discrete Kalman regulator utilizing aKalman filter, as well as with wheel dynamics, the system and method ofthe invention are applicable to real time hydraulic brake systems. Theinvention can also be applied to an electric brake control system withslight modification of dynamic model parameters, gain values andweighting factors.

The terms and definitions set out below in Table 1 are used herein withreference to the equations set out herein.

TABLE 1 Definitions Term Definition Iw mass moment of inertia of atire/wheel/brake w_(n) dynamic model white noise Wt weight per wheel Krratio of torque to pressure r_(r) rolling radius of a tire K controlfeedback gain matrix ref vel reference velocity wheel vel wheel velocitye wheel vel - ref vel x1e: estimated e p_(b) brake pressure x2e:estimated p_(b) (brake pressure) Tb: brake torque v1, v2: measurementwhite noise p_(c) command brake pressure p_(c)* command brake pressureproduced by the Kalman regulator μ coefficient of friction between thetire and runway surface μ* estimated μ value produced by the Kalmanregulator

Table 1 Definitions

As is illustrated in the drawings, the invention is embodied in animproved system 30 for controlling braking of an aircraft duringlanding. Referring to FIG. 1, the system includes a wheel velocitysignal generating means 32, such as a wheel speed transducer, forexample, for producing a wheel velocity signal 34 that is a function ofthe rotational speed of an aircraft wheel, and means 36 for applying acommand brake torque signal based upon a command brake pressure to awheel brake of the aircraft. A brake torque and/or brake pressuretransducer (not shown) is also preferably provided for providing afeedback measurement of one or both of these parameters. A measurementwhite noise (v1) is also an input and summed with the wheel velocitysignal by summer 35. The means for applying a command brake torquesignal typically includes a brake control valve that controls theapplication of pressurized brake fluid from system pressure to the wheelbrake, and may include an amplifier to provide an amplified brakecontrol signal applied to the brake control valve. In a presentlypreferred embodiment, the wheel velocity signal generating means 32further comprises a wheel speed filter 38 for generating a filteredwheel velocity signal 40 based upon the wheel velocity signal.

The improved system for controlling braking of an aircraft duringlanding includes a velocity reference generator 42 for generating areference velocity signal 44 indicating a desired reference velocity.Aircraft velocity comparison means 46 are provided for comparing thewheel velocity signal, which is preferably the filtered wheel velocitysignal 40, with the reference velocity signal 44 for generating avelocity error signal (e) indicative of the difference between theaircraft wheel velocity signal and the reference velocity signal. Anoptimal brake controller 48 is provided for generating an optimal brakepressure control signal 50 for the wheel of the aircraft to cause theaircraft wheel velocity to converge to the desired reference velocity44, based upon an estimated command brake pressure (p_(c)*) and anestimated value of a coefficient of friction (μ*) between the tire andrunway surface. A pressure bias modulator integrator 52 is provided thatis responsive to the wheel velocity signal, which is preferably thefiltered wheel velocity signal 40, and the reference velocity signal 44to provide an antiskid control signal 54. Means 56 are also provided forsumming the optimal brake pressure control signal 50 and the antiskidcontrol signal 54 to produce a command brake pressure signal 58. Thecommand brake pressure signal 58 is also typically amplified by valveamplifier 60 that compensates for a first order hydraulic lag, toprovide an amplified brake control signal 62 applied to the brakecontrol valve 64 that controls the application of pressurized brakefluid from system pressure to the wheel brake according to a referencebrake torque curve correlating the amplified brake control signal to thecorresponding brake torque (Tb) to be applied to the wheel brakes. In apresently preferred embodiment, these functions can be performed by oneor more microprocessors under appropriate software control, althoughalternatively these or analogous functions may be performed by suitablehardware components. Reference information 66 concerning aircraftaerodynamics, nonlinear landing gear dynamics, μ-slip curves and thelike for determining an ultimate drag force to be provided by the wheelbraking, and dynamic model white noise (w_(n)) may also be input to themeans for applying a noisy brake torque signal and a noisy wheelvelocity signal.

As is illustrated in FIGS. 2 and 3, in a presently preferred embodiment,the optimal brake controller 48 comprises a discrete Kalman regulator 70that determines the estimated command brake pressure (p_(c)*) and theestimated value of the coefficient of friction (μ*), based upon input ofto the discrete Kalman regulator of the brake torque signal (Tb), whichmay be summed with a measurement white noise (v2) for the discreteKalman regulator, as well as the wheel velocity signal, which ispreferably the filtered wheel velocity signal, the reference velocitysignal, and measurement white noise (v1). In the optimal brakecontroller, the coefficient of friction (μ*) is preferably adjusted bysuch factors as the weight per wheel (Wt), rolling radius of tire (rr),and the reciprocal of the ratio (Kr) of torque vs. pressure, and issummed by summer 72 with the estimated command brake pressure (p_(c)*),and amplified at 74 by a gain factor to determine the command brakepressure (p_(c)).

With reference to FIG. 3, the discrete Kalman regulator, in a preferredaspect of the invention, comprises a Kalman filter 76 that receives thevelocity error signal (e), which may contain the measurement white noise(v1), and the brake torque signal (Tb), which may contain themeasurement white noise (v2), as well as feedback of the signal outputsof the discrete Kalman regulator, the estimated command brake pressure(p_(c)*) and the estimated value of the coefficient of friction (μ*)between the tire and runway surface. The Kalman filter generates anestimated velocity error signal (x1e) and an estimated brake pressuresignal (x2e), which are received by a control feedback gain matrix 78and which in turn based upon these inputs determines the estimatedcommand brake pressure (p_(c)*) and the estimated value of thecoefficient of friction (μ*) between the tire and runway surface.

A state equation of wheel dynamics used to design a Kalman filterutilized according to the present invention is as follows:$\overset{.}{\omega} = {\left\lbrack {\frac{{Wt} \cdot r_{r}}{I\quad w},{- \frac{1}{I\quad w}}} \right\rbrack \begin{Bmatrix}\mu \\\quad \\{T\quad b}\end{Bmatrix}}$ $\omega = {{\lbrack 1\rbrack \omega} + {\begin{bmatrix}0 & 0\end{bmatrix}\begin{Bmatrix}\mu \\\quad \\{T\quad b}\end{Bmatrix}}}$

where ω is wheel angular velocity (rad/sec); μ is coefficient offriction between the tire and runway surface; Th is brake torque; Wt isweight per wheel; r_(r) is rolling radius of a tire; and Iw is massmoment of inertia of a tire/wheel/brake. The parameters Wt, r_(r), andIw are assumed to be constants for the design of a Kalman regulator.

A first order hydraulic brake pressure lag model maybe described by thefollowing equation:${\overset{.}{p}}_{b} = {\frac{1}{\tau}\left\lbrack {p_{c} - p_{b}} \right\rbrack}$

where p_(b) is brake pressure; p_(c) is brake command pressure; τ istime delay (1×10⁻³ seconds). The torque vs. pressure ratio (Kr) isassumed to be constant for the design of a Kalman regulator.

An augmented linearized state equation from the above equations andassumption is illustrated in FIG. 4, in which the two states (x) are ω(wheel angular velocity) and p_(b) (brake pressure) or Tb (braketorque), w_(n) is dynamic model white noise, and v is output measurementwhite noise. For example, given B-717 parameters and Kr (torque vs.pressure ratio)=20, the augmented state equation is:$\overset{.}{x} = {{\left\lfloor \begin{matrix}0 & {- 2.2272} \\\quad & \quad \\0 & {- 1000.0}\end{matrix} \right\rfloor x} + {\left\lfloor \begin{matrix}{4.0461{e3}} & 0 \\\quad & \quad \\0 & {1.0{e3}}\end{matrix} \right\rfloor u}}$ $y = {{\left\lfloor \begin{matrix}1 & 0 \\\quad & \quad \\0 & 20\end{matrix} \right\rfloor x} + {\left\lfloor \begin{matrix}0 & 0 \\\quad & \quad \\0 & 0\end{matrix} \right\rfloor u}}$

The plant model may be converted to a discrete time model of Ts=5 ms(sampling time) to design a discrete Kalman filter, according to thefollowing equations:

x(k+1)=A·x(k)+B·u(k)+B1·w _(n)(k)

y(k)=C·x(k)+D·u(k)+v(k)

In the design of a Kalman filter, the noise covariance data are given bythe following equations:

E(w _(n)(k)w _(n) ^(T)(k))=Q·δ _(jk)

E(v(k)v ^(T)(k))=R·δ _(jk)

E(w _(n)(k)v ^(T)(k))=N≅0

where E(.) is a mathematical expectation operation, and δ_(jk) is theKronecker delta function.

The Kalman filter equation thus becomes as follows:

q(k)=└A−L(k)CA┘q(k−1)+└B−L(k)CB┘u(k−1+)L(k)y(k)

where q(k) provides the estimated states (x1e, x2e) at k instant.

The Kalman gain matrix L is precalculated, and the control feedback gainmatrix K is also precalculated separately, according to Duality andSeparation property (Linear System Theory and Design, Chen, 1984).

Referring to FIG. 3, the μ* and p_(c)* are control efforts produced bythe Kalman regulator. The term p_(c)* is a brake command pressure; theterm μ* is an estimated μ value that can not be controlled by thecontroller. This value is incorporated into the brake command pressureas is illustrated in the new optimal controller as is illustrated inFIG. 2.

In FIGS. 5 and 6, the reference velocity (REF VEL) of 245 fps isinjected from an external source. The wheel velocity and aircraftvelocity quickly converge to the constant reference velocity (245 fps).As is illustrated in FIG. 6, where e=wheel velocity minus referencevelocity, and p_(b) is the brake pressure, the estimated e and estimatedp_(b) through the Kalman filter are in close agreement with actual e andactual p_(b) values, respectively. The e values (e and estimated e)quickly diminish, so that the wheel velocity quickly follows thereference velocity.

It will be apparent from the foregoing that while particular forms ofthe invention have been illustrated and described, various modificationscan be made without departing from the spirit and scope of theinvention. Accordingly, it is not intended that the invention belimited, except as by the appended claims.

What is claimed is:
 1. In a system for controlling braking of anaircraft during landing, said system including wheel velocity signalgenerating means for producing a wheel velocity signal that is afunction of the rotational speed of a wheel and an associated tire ofthe aircraft, and means for applying a command brake pressure to a wheelbrake of the aircraft, the improvement comprising: a velocity referencegenerator for generating a reference velocity signal indicating adesired reference velocity; aircraft velocity comparison means forcomparing said wheel velocity signal with said reference velocity signalfor generating a velocity error signal indicative of the differencebetween said aircraft wheel velocity signal and said reference velocitysignal; a brake controller for generating a brake pressure controlsignal for the wheel of the aircraft to cause the aircraft wheelvelocity to converge to said reference velocity, based upon an estimatedcommand brake pressure and an estimated value of a coefficient offriction between the tire and runway surface; a pressure bias modulatorresponsive to said wheel velocity signal and said reference velocitysignal to provide an antiskid control signal; and means for summing saidbrake pressure control signal and said antiskid control signal toproduce said command brake pressure signal.
 2. The system of claim 1,wherein said brake controller comprises a discrete Kalman regulator fordetermining the estimated command brake pressure and the estimated valueof the coefficient of friction between the tire and runway surface. 3.The system of claim 2, wherein said discrete Kalman regulator comprisesa control feedback gain matrix and a Kalman filter, said Kalman filterreceiving said velocity error signal and a brake torque feedback signal,and said Kalman filter generating an estimated velocity error signal andan estimated brake pressure, and said control feedback gain matrixreceives said estimated velocity error signal and said estimated brakepressure to generate said estimated command brake pressure and theestimated value of the coefficient of friction between the tire andrunway surface.
 4. The system of claim 1, wherein said wheel velocitysignal generating means comprises a wheel speed filter for generating afiltered wheel velocity signal based upon said wheel velocity signal. 5.In a method controlling braking of an aircraft during landing, themethod including the steps of generating a wheel velocity signal that isa function of the rotational speed of a wheel and an associate tire ofthe aircraft, and applying a command brake torque signal based upon acommand brake pressure to the wheel brake of the aircraft, theimprovement in the method comprising the steps of: generating areference velocity signal indicating a desired reference velocity;comparing said wheel velocity signal with said reference velocity signalfor generating a velocity error signal indicative of the differencebetween said aircraft wheel velocity signal and said reference velocitysignal; generating a brake pressure control signal for the wheel of theaircraft to cause the aircraft wheel velocity to converge to saidreference velocity, based upon an estimated command brake pressure andan estimated value of a coefficient of friction between the tire andrunway surface; providing an antiskid control signal; and summing saidbrake pressure control signal and said antiskid control signal toproduce a command brake pressure signal.
 6. The method of claim 5,wherein said step of generating a brake pressure control signalcomprises determining the estimated command brake pressure and theestimated value of the coefficient of friction with a discrete Kalmanregulator.
 7. The method of claim 6, wherein said discrete Kalmanregulator comprises a control feedback gain matrix and a Kalman filter,said Kalman filter receiving said velocity error signal and a braketorque feedback signal, said Kalman filter generates an estimatedvelocity error signal and an estimated brake pressure, and said controlfeedback gain matrix receives said estimated velocity error signal andsaid estimated brake pressure to generate said estimated command brakepressure and the estimated value of the coefficient of friction betweenthe tire and runway surface.
 8. The method of claim 6, wherein said stepof determining said brake pressure control signal is based upon theestimated value of the coefficient of friction, the weight per wheel,the rolling radius of a tire, the reciprocal of the torque vs. pressureratio, and said estimated command brake pressure.
 9. The method of claim5, wherein said step of generating a wheel velocity signal comprisesfiltering the wheel velocity signal to generate said filtered wheelvelocity signal.